A257556 Triangle, read by rows, T(n,k)= Sum_{i=0..(n-k)/2} C(2*k,i)*C(n-2*i-1,k-1).

1, 1, 1, 3, 2, 1, 3, 7, 3, 1, 4, 12, 12, 4, 1, 4, 23, 28, 18, 5, 1, 4, 34, 66, 52, 25, 6, 1, 4, 49, 126, 143, 85, 33, 7, 1, 4, 64, 228, 328, 265, 128, 42, 8, 1, 4, 80, 372, 700, 701, 444, 182, 52, 9, 1, 4, 96, 573, 1352, 1705, 1320, 693, 248, 63

Offset

1,4

Links

Table of n, a(n) for n=1..64.

Formula

G.f.: (x-1)/((x^5+2*x^3+x)*y+x-1).

Example

1;
1, 1;
3, 2, 1;
3, 7, 3, 1;
4, 12, 12, 4, 1;
4, 23, 28, 18, 5, 1;

Prog

(Maxima)
T(n, k):=sum(binomial(2*k, i)*binomial(n-2*i-1, k-1), i, 0, (n-k)/2);
(PARI) T(n, k)=sum(i=0, (n-k)\2, binomial(2*k, i)*binomial(n-2*i-1, k-1)) \\ Charles R Greathouse IV, Apr 30 2015

Crossrefs

Sequence in context: A147750 A089942 A097409 * A078268 A124782 A106611

Adjacent sequences: A257553 A257554 A257555 * A257557 A257558 A257559

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 29 2015

Status

approved